A normal dye-ink printer cannot be used for t-shirt printing. There are actually some specifications for a printer that must be met before it can be used for shirt printing. These article is about printers for shirt printing using heatpress (a large flat iron).
There are 2 special types of ink that can be used. A sublimation ink and a pigment ink. These kinds of ink cannot be installed in any random printer. It can only be installed using printers with piezoelectric print heads. The printer must also have a Continuous Ink System (CIS) for it to become more efficient for bulk printing.
In a sublimation ink, a sublimation paper is needed. The image must be mirrored before printing. Sublimation printing results to a not so glossy print and looks like the design was painted directly on the shirt (similar to dye printing)
The pigment ink on the other hand needs a transfer paper (light or dark). Light transfer printing is just like sublimation printing except that its color is much stronger than sublimation. It can only be used for white shirts. In dark transfer, the print is like a sticker permanently installed on the shirt. Among the three, it has the highest quality of print except that because of the papers thickness, it is usually “hot” to wear.
Yes, there is the dedicated ink and printers for t-shirt printing. It is also required to have your design layout first and check if it goes through the same as it is. However, myself, I am using offset printing at http://www.digitekprinting.com/offset-printing-2 to works with my business printing needs including t-shirts and giveaways.